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Double Rack and Pinion Problem


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I have a mechanism with two pulleys that are each pin connected to two bodies that are themselves pin connected together. I.e. The centers of all four parts fall within the same plane, axes are parallel, etc.). I would like to add a beam that is rack and pinion connected tangent to the surfaces of both pulleys at all body-to-body angles. For the life of me, I can't figure out how. I can make the rod tangent to both pulleys, but can't use a tangent constraint in a mechanism. I can draw a sketched datum line tangent to the pulleys, but the line is static and does not remain tangent with mechanism motion. Can anyone suggest how this can be done?

O Body to body hinge (pin)
/ \
/ \ Bodies
/ \
O O Pulleys (Pinions)
_______ Beam (Rack)

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